I had an iPhone 5c with this problem. The phone responded to touch by surrounding the text on the screen with a box and speaking the word, or words, displayed. This is an accessibility feature named VoiceOver. There was no response to swiping the screen.
On Apple's support site I found a post by hayblacksupport, with this solution. Tap the home button three times rapidly. This is a shortcut for turning accessibility features on or off. This home button shortcut can be turned on or off in settings.
[http://www.imore.com/how-set-triple-home-click-shortcut-accessibility-iphone-or-ipad]